In the processes of imaging, and particularly in the processes and systems for imaging patients for diagnostic purposes, images are generated by sampling an N dimensional radiation field on a grid of discrete points. The radiation field could be the result of X-ray radiation, nuclear medicine radiation, magnetic resonance radiation, or ultrasound radiation.
The sampling results in initially acquired data which is then transformed by some means to image data. For example, if the imaging system is a tomographic system, then the transformation of the initially acquired data could be a back projection transformation.
Transformation often requires knowledge of image values between sampled grid points; i.e., interpolation. For example, when the transformation is accomplished by back-projecting, then projections of the image from acquired data points are used along with projections of the image from positions between the acquired data points. The projections of the image from positions between acquired data points are supplied using interpolation.
Different types of interpolation techniques may be used. The simplest type, for example, is when the interpolation is made between two neighboring points; then, the effect of each of the neighboring points on the interpolated value is weighted by, for example, both the data amplitude at each of the nearest neighbors and the proximity of the interpolated point to each of its nearest neighbors.
It is important when interpolating that the signal content of the original image be maintained in the interpolated image. Thus, the transformation of the original image into the transformed image must not adversely affect the signal content of the image.
Transformation by interpolation can act either as a low pass or smoothing filter or as a high pass or sharpening filter. This presents a particularly bothersome problem since the sum of all squared interpolation coefficients (the transformation of the "variance") is a location dependent factor. Accordingly, the effect of the low pass or high pass filtering varies over the image as a function of the location relative to the data used for the interpolation.
This variation in the variance as a function of location generates "local texture" artifacts and spectral changes. The local texture artifacts, as the name implies, causes the texture of the image to change as a function of location of the interpolation. The local texture artifact problem is highlighted in a recently published article appearing in the IEEE Transactions on Nulcear Science, Vol. 38, No. 2 (April, 1991) entitled "Variance Propogation for Spect with Energy-Weighted Acquisition" by Ronald J. Jaszczak et al.
To overcome the change in local texture caused by interpolation it would be advantageous to devise an interpolation for which the variance is conserved. This is, in which the interpolation acts neither as a high pass filter nor a low pass filter.